As we had explored in previous classes, division is subtraction again and again and again, multiplication is adding again and again. Exponentiation is multiply again and again and again— They are all inventions to simplify repeated computation.

So is the invention of logarithm: taking log is division again and again and again. They were invented by John Napier who was a Scottish mathematician, physicist, and astronomer in 1614 as a means to simplify calculations.

🙂 Today’s Python numpyclass summary:

Log10 means how many times divide by 10 will return you to 1. log10(100) will give you 2 because 100 divide by 10 twice returns us to one.>>> np.log10(100)
One trillion divide by 10 twelve times returns it to 1.>>> np.log10(1000000000000)

Bonus: Did you know that Engineers and scientists used to use a tool called “slide rule” (计算尺) to do logarithmic computations until 1970s when electronic computer and calculators came into use. You should go and check it out if any of your grandparents have one of these.

We always knew that Chinese parents and teachers are dedicated to education. Even so, we were still amazed by how Chinese teachers and parents are working hand-in-hand pushing the boundaries of education.

We don’t necessarily agree with everything they do, such as the bias towards solving test problems in classes. But there are a great deal more things we agree or appreciate, such as relentless hard work and practice than ones we don’t appreciate.

Below is a snapshot of a first-day summer class for seven year old children. Just look at how intently the parents are. Some parents sat through the entire class to take notes, and some sat in the lounge in the corridor chatting about schools or doing various things while waiting for their kids. The temperature was about 100 degrees outside.

The level of dedication is astonishing.

From time investment perspective, at least one family member, whether mother, father or a grandparent, spends as much as 20 hours and up each week on their children’s education.

From the money side, summer/winter break, weekend, or after-hour schoolings are privately run, which aren’t cheap. Some well-to-do ones have spent hundreds of thousands (measured in US dollars) before high school. Some bold ones even send their kids, sometimes as young as eight or nine years old, to overseas private boarding schools in exclusive locations in Switzerland, the UK and other places. Poorer families still pay for various lessons to make sure their kids are as nourished as possible in education. For those very constraint in resources, such as those parents who must work 7 days a week, we saw their kids studying with video lessons on mobile phones in cram corners instead of hanging out loose.

The primary motivation is the quality of survival for the next generation: to get into top middle schools, top high schools, top universities, great social network and ultimately great jobs in adulthood. Parents start count down of the number of days till college entrance exam even at primary schools. Kids routinely study until mid-night since third grade, and don’t get a day off until winter/summer break.

On the contrary, in United States, students and parents are heard asking for less homework and more free time to play. Over the last two decades, the quality of education, as measured by test scores, have steadily declined in the US. Less work is a key factor. However, a deeper question is: why do American parents and kids want less work from schools? These questions need to be answered by representative data, not ideaologies.